Bisecting an angle

Bisecting an angle is cutting an angle exactly in half.

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Bisecting an angle
To bisect the angle ABC you will need a compass, pencil and a ruler.
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Bisecting an angle
Place your compass on the vertex of the angle, here on point B. Draw an arc that crosses both sides of the angle, lines AB and BC.
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Bisecting an angle
Place your compass on one of the intersection points and draw an arc inside the angle. Do not adjust the compass.
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Bisecting an angle
Place your compass on the other intersection point and draw an arc that cuts the one you just drew.
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Bisecting an angle
Finally, draw a line from the vertex of the angle through the cross you have constructed. You can measure both sides of the angle to check they are equal.
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Bisecting an angle
The line shows all the points that are equidistant from lines AB and BC. The region shaded blue indicates all points that are closer to the line AB than BC, and the area shaded pink contains all points closer to the line BC than AB.

Loci and constructions – WJECBisecting an angle